Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+6y &= 1 \\ -x+4y &= -1\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = x-1$ Divide both sides by $4$ to isolate $y$ $y = {\dfrac{1}{4}x - \dfrac{1}{4}}$ Substitute this expression for $y$ in the first equation. $-7x+6({\dfrac{1}{4}x - \dfrac{1}{4}}) = 1$ $-7x + \dfrac{3}{2}x - \dfrac{3}{2} = 1$ Simplify by combining terms, then solve for $x$ $-\dfrac{11}{2}x - \dfrac{3}{2} = 1$ $-\dfrac{11}{2}x = \dfrac{5}{2}$ $x = -\dfrac{5}{11}$ Substitute $-\dfrac{5}{11}$ for $x$ back into the top equation. $-7( -\dfrac{5}{11})+6y = 1$ $\dfrac{35}{11}+6y = 1$ $6y = -\dfrac{24}{11}$ $y = -\dfrac{4}{11}$ The solution is $\enspace x = -\dfrac{5}{11}, \enspace y = -\dfrac{4}{11}$.